Source: Cyberchase: “A Crinkle in Time”
Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.
In this video segment from Cyberchase, Bianca has been invited to go biking with a friend. Her bike is old, so she goes to a bike shop to buy a new one. While she’s there she learns about gears on bicycles and how they work.
Here are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.
What is Frame, Focus and Follow-up?
Frame: There are many different kinds of bicycles. You may have noticed that bikes have gears. Some bikes have only one gear at the pedal and one gear at the rear wheel. Other bikes have many gears at the rear wheel and sometimes more than one at the pedal as well. What do you think these gears do? How do you think pedals and gears make bikes move?
Focus: As you watch this video segment, you’ll see a bicycle expert explain to Bianca how the gears on her bike work. Write down the two relationships described between the number of teeth on the gear at the pedal and the number of teeth on the gear on the back wheel.
Follow Up: What is the mathematical relationship between the number of teeth on the large gear at the pedal and the number of teeth on the smaller gears at the back wheel? If the gear on the back wheel is replaced with a gear with more teeth, will that gear go around faster or slower than a smaller gear? Why?
KELLY: Hi, Bianca, it's Kelly. The weather is supposed to be nice on Saturday, you want to go biking in Prospect Park?
BIANCA: Well my bike’s a little old.
KELLY: That's OK, my bike isn't great either. Meet you at the main entrance at 10.
BIANCA: OK, sure, I’ll see you there. Kelly has been my best friend since kindergarten. She’s good at everything -- Straight A's, Captain of the soccer team, Homecoming Queen. She’s the best athlete…She’s gonna make me look like I need training wheels. I’ll bet she’ll want to race me and leave me behind on my old bike. I’ll show her.
SALESPERSON: Hi, can I help you?
BIANCA: Hi, I’m looking for a bike with a lot of gears.
SALESPERSON: Sure, come this way. What kind of riding do you do? Road racing, touring, Mountain Biking?
BIANCA: More like Prospect Parking.
SALESPERSON: Here, this is a nice all-round bike.
BIANCA: What do all those gears do?
SALESPERSON: Well, I’ll show you how the gears work with a model. This large gear is like the one on the bike where the pedals are. And this small gear--
BIANCA: ...like the one on the back wheel.
SALESPERSON: Now, when you turn the pedal one time, the front gear turns the back gear a certain number of times. This is what gives you power or speed. Now, count the number of teeth on the big gear.
SALESPERSON: OK, now count the number of teeth on the smaller back wheel gear.
SALESPERSON: How many 12’s are in 36?
SALESPERSON: That means whenever you pedal one time, the back wheel rotates three times. It makes it easier to go uphill. That is the power gear. How many teeth on this one?
SALESPERSON: So that means...
BIANCA: Well let me see. How many 9’s are there in 36? 4. So, that means that the back wheel goes around four times.
SALESPERSON: Right, and that’s the gear for speed.
BIANCA: Speed? That's what I need. I'll be using that gear more.
KELLY: Wow, Bianca that’s a beauty.
BIANCA: Thanks. The gears help me get up hills easily and get a lot of speed on the straightaway.
KELLY: Great! Let's go. Bianca, come back. I don't want to race!
BIANCA: Ha ha!
KELLY: I know your bike can go very fast, but let's just enjoy this beautiful day in the park. You can save racing for another time.
BIANCA: I shouldn't be such a show off. Kelly invited me out and now I left her all alone. That's not very nice.
KELLY: Do you live around here?
HANDSOME GUY: Uh, yeah, a block away.
KELLY: Oh, me too!
HANDSOME GUY: Really?
HANDSOME GUY: Oh, that’s great...
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